Technology for a Changing World

The Department of Applied Mathematics offers an M.S. program in scientific computing and applied mathematics (SciCAM). SciCAM students learn a combination of cutting-edge computational methods for modern high-performance computing architectures and applied mathematical modeling. The department also offers a designated emphasis in Scientific Computing.

The M.S. is ideally suited to meet the increasing need for graduates in the rapidly growing markets of computational mathematics and modeling, high-performance computing and data science. Such computationally knowledgeable and experienced modelers are highly sought after in industry and government agencies.

Applications for admission are handled by the Baskin School of Engineering: gradapp.ucsc.edu/apply/SciCAM-MS/start

Academic questions can be addressed to the current Graduate Director.

Administrative questions can be addressed to the Graduate Advisor.

Scientific Computing and Applied Mathematics MS

Designated Emphasis in Scientific Computing

- 1-year (accelerated) and 2-year (normal) tracks available
- Vast choice of elective courses allows for various specializations
- Research and coursework tracks are both available
- Hands-on approach to scientific computing and applied mathematics
- Practical applied mathematical modeling with real world applications
- Small classes, great student-to-faculty ratio
- Diverse, friendly and supportive faculty
- Potential for internships in Silicon Valley
- Scholarships available

Faculty in Applied Mathematics form the core faculty of the SciCAM program, and have wide-ranging research interests. They teach the majority of SciCAM's core courses, and will be available to advise MS thesis research projects for students on the Thesis track.

- Control Theory: Qi Gong, Abhishek Halder, Marcella Gomez
- Fluid Dynamics: Nic Brummell, Pascale Garaud, Dongwook Lee, Daniele Venturi
- High-performance computing: Nic Brummell, Dongwook Lee, Daniele Venturi
- Stochastic Modeling: Daniele Venturi, Hongyun Wang, Abhishek Halder
- Mathematical Biology: Hongyun Wang, Marcella Gomez

The Department of Applied Mathematics and Statistics is also home to many other faculty with specialization in Bayesian Statistics, who teach some of SciCAM's elective courses and may be available to co-advise MS thesis research projects. The complete list of AMS faculty is available here.

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All students must complete the Core and Foundational courses described below.

Core & Foundational Requirements |
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AMS 212A |

AMS 213A |

AMS 213B |

AMS 214 |

AMS 250 |

Students in the SciCAM program **must also demonstrate mastery in the foundations of Scientific Computing and Applied Mathematics**, either by producing evidence through undergraduate transcripts, or by taking some or all of the following foundational courses upon entry to the M.S. program: AMS 147 (Computational Methods and Applications), AMS 129 (Foundations of Scientific Computing) and AMS 211 (Foundations of Applied Mathematics).

**Approved elective courses: ** Any regular graduate AMS course not already in the core except AMS 200 and supervised research courses; a list of current allowable electives in other departments is maintained by the graduate director, and updated on a yearly basis. Students may also petition the program to add one or more courses to the elective list. Note that some upper division electives are allowed, bearing in mind that no more than a total of 15 units of upper division courses may be used to satisfy the degree requirements.

Students in the SciCAM program may pursue a **Plan I** (thesis capstone) or a **Plan II** (comprehensive examination capstone) curriculum.

**Candidates for a Plan I** capstone must, in addition to the 25 units required from core courses,

(1) complete one additional 5-unit course from the approved elective list,

(2) complete 10 units of supervised research (in the form of AMS 297 or AMS 298 with one of the program faculty), and

(3) write a thesis.

**The thesis requirements are as follows: **

Students must submit a thesis proposal to the potential faculty sponsor after completion of all core courses. If the proposal is accepted, the faculty member will become the sponsor and will supervise the research and writing of the thesis project. The project will involve the solution of a problem or problems from the selected area of application. The thesis must consist of at least 30 pages and no more than 60 pages of printed written work and accompanying pertinent figures, consisting of a coherent introduction and presentation of the current state of the field, a clear presentation of the questions raised, of the methodology used to solve them, and a discussion of the results obtained. The thesis will be read by at least three faculty from the AMS department, one of which must be the student’s adviser. The student will then be required to give a short (20 minute) public oral presentation of their thesis, which will be evaluated by the reading committee. The reading committee will assess the quality of both written work and oral presentation in making their recommendation for awarding the M.S. degree to the student.

**Candidates for a Plan II** capstone must, in addition to the 25 units required from core courses,

(1) complete three additional 5-unit courses from the approved elective list, and

(2) successfully pass the SciCAM comprehensive examination.

The latter takes place in June at the end of the academic year. Students may only take this exam following completion of the last core course. The exam will take the form of a take-home project covering all core and foundational courses.

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The expected time to completion of the SciCAM degree program is two years. However, AMS also offers a one year accelerated track for interested students who can demonstrate sufficient proficiency in the foundational subjects. Information on the minimum requirements to join the accelerated track can be found on the program website. Requests to join the accelerated track must be made to the graduate director by email no later than August 31^{st} of each year.

Students in the SciCAM M.S. program interested in an academic career will be strongly encouraged to apply to the SAM Ph.D. program. Applications are reviewed in the standard academic cycle, so that students interested in applying to the SAM program are encouraged to discuss this option with the graduate director in the fall of each year.

Up to three UCSC courses fulfilling the degree requirements of the SciCAM degree may be taken before beginning the graduate program.

Up to one course from other institutions may be applied to the M.S. degree course requirements. Petitions should be submitted along with the transcript from the other institution or UCSC Extension. For courses taken at other institutions, copies of the syllabi, exams, and other course work should accompany the petition. Such petitions are not considered until the completion of at least one quarter at UCSC.

Each year, the faculty reviews the progress of every student in all programs and tracks. Students not making adequate progress toward completion of degree requirements are subject to dismissal from the program (see the Graduate Handbook for the policy on satisfactory academic progress). For specific guidelines on the annual student reviews, please refer to: http://www.soe.ucsc.edu/programs/ssm/graduate/index.html

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- The ability to take a real-life science or engineering problem, and create a mathematical model of it, under supervision or with the help of discussions with colleagues.
- Proficiency in analytical methods for the solution of linear algebra problems, ordinary and partial differential equations.
- Proficiency in the construction of numerical algorithms for the solution of linear algebra problems, as well as ordinary and partial differential equations.
- Proficiency in at least 2 scientific computing languages such as: Fortran, C, Python, R, Matlab, etc. Familiarity with Unix-type operating systems, the use of compilers, professional scientific computing libraries, efficient IO algorithms, data visualization tools, etc.
- Proficiency in the two main parallel computing paradigms (shared vs. distributed memory) and in the use of OpenMP and MPI. Familiarity with parallel architectures and with supercomputing environments such as batch submission scripts, data transfer protocols, scripting, etc.
- The ability to identify and implement, among all of the methods and languages known, the most appropriate and efficient approach for the original problem posed.
- The ability to analyze critically the results from the model obtained, and to present them clearly and coherently to peers (orally and/or in writing).

The progress of each student towards the PLOs will be monitored by the program faculty through:

- regular formative and summative assessments in the classroom context (participation, homework, quizzes, midterms),
- final examinations or final projects in each of the individual core courses,
- the comprehensive capstone requirement (whether Thesis or Comprehensive exam).

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Students from another degree program who meet certain requirements (see below) can have the designated emphasis of “Scientific Computing” annotated to their degree title. For example, a M.S. or Ph.D. student in physics who meets the requirements would get a certification that read “M.S. Physics (Scientific Computing) or “Ph.D. Physics (Scientific Computing).” Upon electing to pursue a designated emphasis (DE) in scientific computing, students must choose a DE faculty adviser in the AMS Department. A list of eligible DE advisers is maintained online. The student must organize a preliminary meeting with the DE adviser, and agree on a plan for completion of the requirements. Once this plan has been designed, the student and the adviser must complete the Application for a Designated Emphasis in Scientific Computing form available online. The completed application form should then be signed by the AMS graduate director, and filed in the BSOE Graduate Advising Office (bsoe-ga@rt.ucsc.edu). This should be done before the student’s advancement to candidacy (for Ph.D. students), and no later than three months before the planned date for the oral presentation completion requirement (see below).

**Course requirements:** AMS 213A (Numerical Linear Algebra), AMS 213B (Numerical Solutions of Differential Equations), AMS 250 (Introduction to High-Performance Computing), as well as one additional course from the following list of approved electives: AMS 260, CMPS 201, CMPS 211, CMPS 242, CMPS 261, and AST 235.

**Writing requirements:** a substantial and original written body of work related to scientific computing, associated with substantial code development. or substantial modification of existing code, or development of significant computational tools for data analysis. The write-up could take the form of a paper (at least submitted), or an M.S., M.A. or Ph.D. thesis chapter, for instance.

**Oral presentation requirement:** a presentation of no less than 30 minutes during which the student must demonstrate mastery of the scientific computing component of the submitted written piece of work. This presentation could be the student’s qualifying exam, or the Ph.D. defense, or a separate presentation. The DE adviser must be invited to attend this presentation.

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Attachment | Size |
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SciCAM Poster | 474.61 KB |